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ОбложкаKleppner D. An introduction to mechanics / D.Kleppner, R.J.Kolenkow. - Cambridge; New York: Cambridge University Press, 2010. - xxii, 546 p. - Ind.: p.540-546. - ISBN 978-0-521-19821-9
Шифр: (И/B2-K54) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
LIST OF EXAMPLES ............................................... xi
PREFACE ........................................................ xv
TO THE TEACHER ................................................ xix

1  VECTORS AND KINEMATICS - A FEW MATHEMATICAL PRELIMINARIES
   1.1  INTRODUCTION ............................................ 2
   1.2  VECTORS ................................................. 2
        Definition of a Vector, The Algebra of Vectors .......... 3
   1.3  COMPONENTS OF A VECTOR .................................. 8
   1.4  BASE VECTORS ........................................... 10
   1.5  DISPLACEMENT AND THE POSITION VECTOR ................... 11
   1.6  VELOCITY AND ACCELERATION .............................. 13
        Motion in One Dimension ................................ 14
        Motion in Several Dimensions ........................... 14
        A Word about Dimensions and Units ...................... 18
   1.7  FORMAL SOLUTION OF KINEMATICAL EQUATIONS ............... 19
   1.8  MORE ABOUT THE DERIVATIVE OF A VECTOR .................. 23
   1.9  MOTION IN PLANE POLAR COORDINATES ...................... 27
        Polar Coordinates ...................................... 27
        Velocity in Polar Coordinates .......................... 27
        Evaluating dr/dt ....................................... 31
        Acceleration in Polar Coordinates ...................... 36
   Note 1.1 MATHEMATICAL APPROXIMATION METHODS ................. 39
        The Binomial Series .................................... 41
        Taylor's Series ........................................ 42
        Differentials .......................................... 45
        Some References to Calculus Texts ...................... 47
   PROBLEMS .................................................... 47

2  NEWTON'S LAWS - THE FOUNDATIONS OF NEWTONIAN MECHANICS
   2.1  INTRODUCTION ........................................... 52
   2.2  NEWTON'S LAWS .......................................... 53
   Newton's First Law .......................................... 55
        Newton's Second Law .................................... 56
        Newton's Third Law ..................................... 59
   2.3  STANDARDS AND UNITS .................................... 64
        The Fundamental Standards .............................. 64
        Systems of Units ....................................... 67
   2.4  SOME APPLICATIONS OF NEWTON'S LAWS ..................... 68
   2.5  THE EVERYDAY FORCES OF PHYSICS ......................... 79
        Gravity, Weight, and the Gravitational Field ........... 80
        The Electrostatic Force ................................ 86
        Contact Forces ......................................... 87
        Tension—The Force of a String .......................... 87
        Tension and Atomic Forces .............................. 91
        The Normal Force ....................................... 92
        Friction ............................................... 92
        Viscosity .............................................. 95
        The Linear Restoring Force: Hooke's Law, the Spring,
        and Simple Harmonic Motion ............................. 97
   Note 2.1 THE GRAVITATIONAL ATTRACTION OF A SPHERICAL
        SHELL ................................................. 101
   PROBLEMS ................................................... 103

3  MOMENTUM
   3.1  INTRODUCTION .......................................... 112
   3.2  DYNAMICS OF A SYSTEM OF PARTICLES ..................... 113
        Center of Mass ........................................ 116
   3.3  CONSERVATION OF MOMENTUM .............................. 122
        Center of Mass Coordinates ............................ 127
   3.4  IMPULSE AND A RESTATEMENT OF THE MOMENTUM RELATION .... 130
   3.5  MOMENTUM AND THE FLOW OF MASS ......................... 133
   3.6  MOMENTUM TRANSPORT .................................... 139
   Note 3.1 CENTER OF MASS .................................... 145
   PROBLEMS ................................................... 147

4  WORK AND ENERGY
   4.1  INTRODUCTION .......................................... 152
   4.2  INTEGRATING THE EQUATION OF MOTION IN ONE DIMENSION ... 153
   4.3  THE WORK-ENERGY THEOREM IN ONE DIMENSION .............. 156
   4.4  INTEGRATING THE EQUATION OF MOTION IN SEVERAL
        DIMENSIONS ............................................ 158
   4.5  THE WORK-ENERGY THEOREM ............................... 160
   4.6  APPLYING THE WORK-ENERGY THEOREM ...................... 162
   4.7  POTENTIAL ENERGY 168 Illustrations of Potential
        Energy ................................................ 170
   4.8  WHAT POTENTIAL ENERGY TELLS US ABOUT FORCE ............ 173
        Stability ............................................. 174
   4.9  ENERGY DIAGRAMS ....................................... 176
   4.10 SMALL OSCILLATIONS IN A BOUND SYSTEM .................. 178
   4.11 NONCONSERVATIVE FORCES ................................ 182
   4.12 THE GENERAL LAW OF CONSERVATION OF ENERGY ............. 184
   4.13 POWER ................................................. 186
   4.14 CONSERVATION LAWS AND PARTICLE COLLISIONS ............. 187
        Collisions and Conservation Laws ...................... 188
        Elastic and Inelastic Collisions ...................... 188
        Collisions in One Dimension ........................... 189
        Collisions and Center of Mass Coordinates ............. 190
   PROBLEMS ................................................... 194

5  SOME MATHEMATICAL ASPECTS OF FORCE AND ENERGY
   5.1  INTRODUCTION .......................................... 202
   5.2  PARTIAL DERIVATIVES ................................... 202
   5.3  HOW TO FIND THE FORCE IF YOU KNOW THE POTENTIAL
        ENERGY ................................................ 206
   5.4  THE GRADIENT OPERATOR ................................. 207
   5.5  THE PHYSICAL MEANING OF THE GRADIENT .................. 210
        Constant Energy Surfaces and Contour Lines ............ 211
   5.6  HOW TO FIND OUT IF A FORCE IS CONSERVATIVE ............ 215
   5.7  STOKES' THEOREM ....................................... 225
   PROBLEMS ................................................... 228

6  ANGULAR MOMENTUM AND FIXED AXIS ROTATION
   6.1  INTRODUCTION .......................................... 232
   6.2  ANGULAR MOMENTUM OF A PARTICLE ........................ 233
   6.3  TORQUE ................................................ 238
   6.4  ANGULAR MOMENTUM AND FIXED AXIS ROTATION .............. 248
   6.5  DYNAMICS OF PURE ROTATION ABOUT AN AXIS ............... 253
   6.6  THE PHYSICAL PENDULUM ................................. 255
        The Simple Pendulum ................................... 253
        The Physical Pendulum ................................. 257
   6.7  MOTION INVOLVING BOTH TRANSLATION AND ROTATION ........ 260
        The Work-energy Theorem ............................... 267
   6.8  THE BOHR ATOM ......................................... 270
   Note 6.1 CHASLES'THEOREM ................................... 274
   Note 6.2 PENDULUM MOTION ................................... 276
   PROBLEMS ................................................... 279

7  RIGID BODY MOTION AND THE CONSERVATION OF ANGULAR MOMENTUM
   7.1  INTRODUCTION .......................................... 288
   7.2  THE VECTOR NATURE OF ANGULAR VELOCITY AND ANGULAR
        MOMENTUM .............................................. 288
   7.3  THE GYROSCOPE ......................................... 295
   7.4  SOME APPLICATIONS OF GYROSCOPE MOTION ................. 300
   7.5  CONSERVATION OF ANGULAR MOMENTUM ...................... 305
   7.6  ANGULAR MOMENTUM OF A ROTATING RIGID BODY ............. 308
        Angular Momentum and the Tensor of Inertia ............ 308
        Principal Axes ........................................ 313
        Rotational Kinetic Energy ............................. 313
        Rotation about a Fixed Point .......................... 315
   7.7  ADVANCED TOPICS IN THE DYNAMICS OF RIGID BODY
        ROTATION .............................................. 316
        Introduction .......................................... 316
        Torque-free Precession: Why the Earth Wobbles ......... 317
        Euler's Equations ..................................... 320
    Note 7.1 FINITE AND INFINITESIMAL ROTATIONS ............... 326
    Note 7.2 MORE ABOUT GYROSCOPES ............................ 328
        Case 1 Uniform Precession ............................. 331
        Case 2 Torque-free Precession ......................... 331
        Case 3 Nutation ....................................... 331
    PROBLEMS .................................................. 334

8  NONINERTIAL SYSTEMS AND FICTITIOUS FORCES
   8.1  INTRODUCTION .......................................... 340
   8.2  THE GALILEAN TRANSFORMATIONS .......................... 340
LIST OF EXAMPLES ............................................... xi
PREFACE ........................................................ xv
TO THE TEACHER ................................................ xix

1  VECTORS AND KINEMATICS - A FEW MATHEMATICAL PRELIMINARIES
   1.1  INTRODUCTION ............................................ 2
   1.2  VECTORS ................................................. 2
        Definition of a Vector, The Algebra of Vectors .......... 3
   1.3  COMPONENTS OF A VECTOR .................................. 8
   1.4  BASE VECTORS ........................................... 10
   1.5  DISPLACEMENT AND THE POSITION VECTOR ................... 11
   1.6  VELOCITY AND ACCELERATION .............................. 13
        Motion in One Dimension ................................ 14
        Motion in Several Dimensions ........................... 14
        A Word about Dimensions and Units ...................... 18
   1.7  FORMAL SOLUTION OF KINEMATICAL EQUATIONS ............... 19
   1.8  MORE ABOUT THE DERIVATIVE OF A VECTOR .................. 23
   1.9  MOTION IN PLANE POLAR COORDINATES ...................... 27
        Polar Coordinates ...................................... 27
        Velocity in Polar Coordinates .......................... 27
        Evaluating dr/dt ....................................... 31
        Acceleration in Polar Coordinates ...................... 36
   Note 1.1 MATHEMATICAL APPROXIMATION METHODS ................. 39
        The Binomial Series .................................... 41
        Taylor's Series ........................................ 42
        Differentials .......................................... 45
        Some References to Calculus Texts ...................... 47
   PROBLEMS .................................................... 47

2  NEWTON'S LAWS - THE FOUNDATIONS OF NEWTONIAN MECHANICS
   2.1  INTRODUCTION ........................................... 52
   2.2  NEWTON'S LAWS .......................................... 53
   Newton's First Law .......................................... 55
        Newton's Second Law .................................... 56
        Newton's Third Law ..................................... 59
   2.3  STANDARDS AND UNITS .................................... 64
        The Fundamental Standards .............................. 64
        Systems of Units ....................................... 67
   2.4  SOME APPLICATIONS OF NEWTON'S LAWS ..................... 68
   2.5  THE EVERYDAY FORCES OF PHYSICS ......................... 79
        Gravity, Weight, and the Gravitational Field ........... 80
        The Electrostatic Force ................................ 86
        Contact Forces ......................................... 87
        Tension—The Force of a String .......................... 87
        Tension and Atomic Forces .............................. 91
        The Normal Force ....................................... 92
        Friction ............................................... 92
        Viscosity .............................................. 95
        The Linear Restoring Force: Hooke's Law, the Spring,
        and Simple Harmonic Motion ............................. 97
   Note 2.1 THE GRAVITATIONAL ATTRACTION OF A SPHERICAL
        SHELL ................................................. 101
   PROBLEMS ................................................... 103

3  MOMENTUM
   3.1  INTRODUCTION .......................................... 112
   3.2  DYNAMICS OF A SYSTEM OF PARTICLES ..................... 113
        Center of Mass ........................................ 116
   3.3  CONSERVATION OF MOMENTUM .............................. 122
        Center of Mass Coordinates ............................ 127
   3.4  IMPULSE AND A RESTATEMENT OF THE MOMENTUM RELATION .... 130
   3.5  MOMENTUM AND THE FLOW OF MASS ......................... 133
   3.6  MOMENTUM TRANSPORT .................................... 139
   Note 3.1 CENTER OF MASS .................................... 145
   PROBLEMS ................................................... 147

4  WORK AND ENERGY
   4.1  INTRODUCTION .......................................... 152
   4.2  INTEGRATING THE EQUATION OF MOTION IN ONE DIMENSION ... 153
   4.3  THE WORK-ENERGY THEOREM IN ONE DIMENSION .............. 156
   4.4  INTEGRATING THE EQUATION OF MOTION IN SEVERAL
        DIMENSIONS ............................................ 158
   4.5  THE WORK-ENERGY THEOREM ............................... 160
   4.6  APPLYING THE WORK-ENERGY THEOREM ...................... 162
   4.7  POTENTIAL ENERGY 168 Illustrations of Potential
        Energy ................................................ 170
   4.8  WHAT POTENTIAL ENERGY TELLS US ABOUT FORCE ............ 173
        Stability ............................................. 174
   4.9  ENERGY DIAGRAMS ....................................... 176
   4.10 SMALL OSCILLATIONS IN A BOUND SYSTEM .................. 178
   4.11 NONCONSERVATIVE FORCES ................................ 182
   4.12 THE GENERAL LAW OF CONSERVATION OF ENERGY ............. 184
   4.13 POWER ................................................. 186
   4.14 CONSERVATION LAWS AND PARTICLE COLLISIONS ............. 187
        Collisions and Conservation Laws ...................... 188
        Elastic and Inelastic Collisions ...................... 188
        Collisions in One Dimension ........................... 189
        Collisions and Center of Mass Coordinates ............. 190
   PROBLEMS ................................................... 194

5  SOME MATHEMATICAL ASPECTS OF FORCE AND ENERGY
   5.1  INTRODUCTION .......................................... 202
   5.2  PARTIAL DERIVATIVES ................................... 202
   5.3  HOW TO FIND THE FORCE IF YOU KNOW THE POTENTIAL
        ENERGY ................................................ 206
   5.4  THE GRADIENT OPERATOR ................................. 207
   5.5  THE PHYSICAL MEANING OF THE GRADIENT .................. 210
        Constant Energy Surfaces and Contour Lines ............ 211
   5.6  HOW TO FIND OUT IF A FORCE IS CONSERVATIVE ............ 215
   5.7  STOKES' THEOREM ....................................... 225
   PROBLEMS ................................................... 228

6  ANGULAR MOMENTUM AND FIXED AXIS ROTATION
   6.1  INTRODUCTION .......................................... 232
   6.2  ANGULAR MOMENTUM OF A PARTICLE ........................ 233
   6.3  TORQUE ................................................ 238
   6.4  ANGULAR MOMENTUM AND FIXED AXIS ROTATION .............. 248
   6.5  DYNAMICS OF PURE ROTATION ABOUT AN AXIS ............... 253
   6.6  THE PHYSICAL PENDULUM ................................. 255
        The Simple Pendulum ................................... 253
        The Physical Pendulum ................................. 257
   6.7  MOTION INVOLVING BOTH TRANSLATION AND ROTATION ........ 260
        The Work-energy Theorem ............................... 267
   6.8  THE BOHR ATOM ......................................... 270
   Note 6.1 CHASLES'THEOREM ................................... 274
   Note 6.2 PENDULUM MOTION ................................... 276
   PROBLEMS ................................................... 279

7  RIGID BODY MOTION AND THE CONSERVATION OF ANGULAR MOMENTUM
   7.1  INTRODUCTION .......................................... 288
   7.2  THE VECTOR NATURE OF ANGULAR VELOCITY AND ANGULAR
        MOMENTUM .............................................. 288
   7.3  THE GYROSCOPE ......................................... 295
   7.4  SOME APPLICATIONS OF GYROSCOPE MOTION ................. 300
   7.5  CONSERVATION OF ANGULAR MOMENTUM ...................... 305
   7.6  ANGULAR MOMENTUM OF A ROTATING RIGID BODY ............. 308
        Angular Momentum and the Tensor of Inertia ............ 308
        Principal Axes ........................................ 313
        Rotational Kinetic Energy ............................. 313
        Rotation about a Fixed Point .......................... 315
   7.7  ADVANCED TOPICS IN THE DYNAMICS OF RIGID BODY
        ROTATION .............................................. 316
        Introduction .......................................... 316
        Torque-free Precession: Why the Earth Wobbles ......... 317
        Euler's Equations ..................................... 320
    Note 7.1 FINITE AND INFINITESIMAL ROTATIONS ............... 326
    Note 7.2 MORE ABOUT GYROSCOPES ............................ 328
        Case 1 Uniform Precession ............................. 331
        Case 2 Torque-free Precession ......................... 331
        Case 3 Nutation ....................................... 331
    PROBLEMS .................................................. 334

8  NONINERTIAL SYSTEMS AND FICTITIOUS FORCES
   8.1  INTRODUCTION .......................................... 340
   8.2  THE GALILEAN TRANSFORMATIONS .......................... 340
8.3  UNIFORMLY ACCELERATING SYSTEMS ........................ 343
   8.4  THE PRINCIPLE OF EQUIVALENCE .......................... 346
   8.5  PHYSICS IN A ROTATING COORDINATE SYSTEM ............... 355
        Time Derivatives and Rotating Coordinates ............. 356
        Acceleration Relative to Rotating Coordinates ......... 358
        The Apparent Force in a Rotating Coordinate System .... 359
   Note 8.1  THE EQUIVALENCE PRINCIPLE AND THE
        GRAVITATIONAL RED SHIFT ............................... 369
   Note 8.2  ROTATING COORDINATE TRANSFORMATION ............... 371
   PROBLEMS ................................................... 372

9  CENTRAL FORCE MOTION
   9.1  INTRODUCTION .......................................... 378
   9.2  CENTRAL FORCE MOTION AS A ONE BODY PROBLEM ............ 378
   9.3  GENERAL PROPERTIES OF CENTRAL FORCE MOTION ............ 380
        The Motion Is Confined to a Plane ..................... 380
        The Energy and Angular Momentum Are Constants of the
        Motion ................................................ 380
        The Law of Equal Areas ................................ 382
   9.4  FINDING THE MOTION IN REAL PROBLEMS ................... 382
   9.5  THE ENERGY EQUATION AND ENERGY DIAGRAMS ............... 383
   9.6  PLANETARY MOTION ...................................... 390
   9.7  KEPLER'S LAWS ......................................... 400
   Note 9.1 PROPERTIES OF THE ELLIPSE ......................... 403
   PROBLEMS ................................................... 406

10 THE HARMONIC OSCILLATOR
   10.1 INTRODUCTION AND REVIEW ............................... 410
        Standard Form of the Solution ......................... 410
        Nomenclature .......................................... 411
        Energy Considerations ................................. 412
        Time Average Values ................................... 413
        Average Energy ........................................ 413
   10.2 THE DAMPED HARMONIC OSCILLATOR ........................ 414
        Energy ................................................ 416
        The Q of an Oscillator ................................ 418
   10.3 THE FORCED HARMONIC OSCILLATOR ........................ 421
        The Undamped Forced Oscillator ........................ 421
        Resonance ............................................. 423
        The Forced Damped Harmonic Oscillator ................. 424
        Resonance in a Lightly Damped System: The Quality
        Factor Q .............................................. 426
   10.4 RESPONSE IN TIME VERSUS RESPONSE IN FREQUENCY ......... 432
   Note 10.1  SOLUTION OF THE EQUATION OF MOTION FOR
        THE UNDRIVEN DAMPED OSCILLATOR ........................ 433
        The Use of Complex Variables .......................... 433
        The Damped Oscillator ................................. 435
   Note 10.2 SOLUTION OF THE EQUATION OF MOTION FOR
        THE FORCED OSCILLATOR ................................. 437
   PROBLEMS ................................................... 438

11 THE SPECIAL THEORY OF RELATIVITY
   11.1 THE NEED FOR A NEW MODE OF THOUGHT .................... 442
   11.2 THE MICHELSON-MORLEY EXPERIMENT ....................... 445
   11.3 THE POSTULATES OF SPECIAL RELATIVITY .................. 450
        The Universal Velocity ................................ 451
        The Principle of Relativity ........................... 451
        The Postulates of special Relativity .................. 452
   11.4 THE GALILEAN TRANSFORMATIONS .......................... 453
   11.5 THE LORENTZ TRANSFORMATIONS ........................... 455
   PROBLEMS ................................................... 459

12 RELATIVISTIC KINEMATICS
   12.1 INTRODUCTION .......................................... 462
   12.2 SIMULTANEITY AND THE ORDER OF EVENTS .................. 463
   12.3 THE LORENTZ CONTRACTION AND TIME DILATION ............. 466
        The Lorentz Contraction ............................... 466
        Time Dilation ......................................... 468
   12.4 THE RELATIVISTIC TRANSFORMATION OF VELOCITY ........... 472
   12.5 THE DOPPLER EFFECT .................................... 475
        The Doppler Shift in Sound ............................ 475
        Relativistic Doppler Effect ........................... 477
        The Doppler Effect for an Observer off the Line of
        Motion ................................................ 478
   12.6 THE TWIN PARADOX ...................................... 480
   PROBLEMS ................................................... 484

13 RELATIVISTIC MOMENTUM AND ENERGY
   13.1 MOMENTUM .............................................. 490
   13.2 ENERGY ................................................ 493
   13.3 MASSLESS PARTICLES .................................... 500
   13.4 DOES LIGHT TRAVEL AT THE VELOCITY OF LIGHT? ........... 508
   PROBLEMS ................................................... 512

14 FOUR-VECTORS AND RELATIVISTIC INVARIANCE
   14.1 INTRODUCTION .......................................... 516
   14.2 VECTORS AND TRANSFORMATIONS ........................... 516
        Rotation about the z Axis ............................. 517
        Invariants of a Transformation ........................ 520
        The Trans-   formation Properties of Physical Laws .... 520
        Scalar Invariants ..................................... 521
   14.3 MINIKOWSKI SPACE AND FOUR-VECTORS ..................... 521
   14.4 THE MOMENTUM-ENERGY FOUR-VECTOR ....................... 527
   14.5 CONCLUDING REMARKS .................................... 534
   PROBLEMS ................................................... 536

INDEX ......................................................... 539

LIST OF EXAMPLES

1  VECTORS AND KINEMATICS - A FEW MATHEMATICAL PRELIMINARIES
   EXAMPLES, CHAPTER 1
   1.1  Law of Cosines .......................................... 5
   1.2  Work and the Dot Product ................................ 5
   1.3  Examples of the Vector Product in Physics ............... 7
   1.4  Area as a Vector ........................................ 7
   1.5  Vector Algebra .......................................... 9
   1.6  Construction of a Perpendicular Vector ................. 10
   1.7  Finding v from r ....................................... 16
   1.8  Uniform Circular Motion ................................ 17
   1.9  Finding Velocity from Acceleration ..................... 20
   1.10 Motion in a Uniform Gravitational Field ................ 21
   1.11 Nonuniform Acceleration—The Effect of a Radio Wave on
        an Ionospheric Electron ................................ 22
   1.12 Circular Motion and Rotating 
Vectors ................... 25
1.13 Circular Motion and Straight Line Motion in Polar
        Coordinates ............................................ 34
   1.14 Velocity of a Bead on a Spoke .......................... 35
   1.15 Off-center Circle ...................................... 35
   1.16 Acceleration of a Bead on a Spoke ...................... 37
   1.17 Radial Motion without Acceleration ..................... 38

2  NEWTON'S LAWS—THE FOUNDATIONS OF NEWTONIAN MECHANICS
   EXAMPLES, CHAPTER 2
   2.1  Astronauts in Space—Inertial Systems and Fictitious
        Force .................................................. 60
   2.2  The Astronauts' Tug-of-war ............................. 70
   2.3  Freight Train .......................................... 72
   2.4  Constraints ............................................ 74
   2.5  Block on String 1 ...................................... 75
   2.6  Block on String 2 ...................................... 76
   2.7  The Whirling Block ..................................... 76
   2.8  The Conical Pendulum ................................... 77
   2.9  Turtle in an Elevator .................................. 84
   2.10 Block and String 3 ..................................... 87
   2.11 Dangling Rope .......................................... 88
   2.12 Whirling Rope .......................................... 89
   2.13 Pulleys ................................................ 90
   2.14 Block and Wedge with Friction .......................... 93
   2.15 The Spinning Terror .................................... 94
   2.16 Free Motion in a Viscous Medium ........................ 96
   2.17 Spring and Block—The Equation for Simple Harmonic
        Motion ................................................. 98
   2.18 The Spring Gun - An Example Illustrating Initial
        Conditions ............................................. 99

3  MOMENTUM
   EXAMPLES, CHAPTER 3
   3.1  The Bola .............................................. 115
   3.2  Drum Major's Baton .................................... 117
   3.3  Center of Mass of a Nonuniform Rod .................... 119
   3.4  Center of Mass of a Triangular Sheet .................. 120
   3.5  Center of Mass Motion ................................. 122
   3.6  Spring Gun Recoil ..................................... 123
   3.7  Earth, Moon, and Sun - A Three Body System ............ 125
   3.8  The Push Me-Pull You .................................. 128
   3.9  Rubber Ball Rebound ................................... 131
   3.10 How to Avoid Broken Ankles ............................ 132
   3.11 Mass Flow and Momentum ................................ 134
   3.12 Freight Car and Hopper ................................ 135
   3.13 Leaky Freight Car ..................................... 136
   3.14 Rocket in Free Space .................................. 138
   3.15 Rocket in a Gravitational Field ....................... 139
   3.16 Momentum Transport to a Surface ....................... 141
   3.17 A Dike at the Bend of a River ......................... 143
   3.18 Pressure of a Gas ..................................... 144

4  WORK AND ENERGY
   EXAMPLES, CHAPTER 4
   4.1  Mass Thrown Upward in a Uniform Gravitational Field ... 154
   4.2  Solving the Equation of Simple Harmonic Motion ........ 154
   4.3  Vertical Motion in an Inverse Square Field ............ 156
   4.4  The Conical Pendulum .................................. 161
   4.5  Escape Velocity—The General Case ...................... 162
   4.6  The Inverted Pendulum ................................. 164
   4.7  Work Done by a Uniform Force .......................... 165
   4.8  Work Done by a Central Force .......................... 167
   4.9  A Path-dependent Line Integral ........................ 167
   4.10 Parametric Evaluation of a Line Integral .............. 168
   4.11 Potential Energy of a Uniform Force Field ............. 170
   4.12 Potential Energy of an Inverse Square Force ........... 171
   4.13 Bead, Hoop, and Spring ................................ 172
   4.14 Energy and Stability - The Teeter Toy ................. 175
   4.15 Molecular Vibrations .................................. 179
   4.16 Small Oscillations .................................... 181
   4.17 Block Sliding down Inclined Plane ..................... 183
   4.18 Elastic Collision of Two Balls ........................ 190
   4.19 Limitations on Laboratory Scattering Angle ............ 193

5  SOME MATHEMATICAL ASPECTS OF FORCE AND ENERGY
   EXAMPLES, CHAPTER 5
   5.1  Partial Derivatives ................................... 203
   5.2  Applications of the Partial Derivative ................ 205
   5.3  Gravitational Attraction by a Particle ................ 208
   5.4  Uniform Gravitational Field ........................... 209
   5.5  Gravitational Attraction by Two Point Masses .......... 209
   5.6  Energy Contours for a Binary Star System .............. 212
   5.7  The Curl of the Gravitational Force ................... 219
   5.8  A Nonconservative Force ............................... 220
   5.9  A Most Unusual Force Field ............................ 221
   5.10 Construction of the Potential Energy Function ......... 222
   5.11 How the Curl Got Its Name ............................. 224
   5.12 Using Stokes' Theorem ................................. 227

6  ANGULAR MOMENTUM AND FIXED AXIS ROTATION
   EXAMPLES, CHAPTER 6
   6.1  Angular Momentum of a Sliding Block ................... 236
   6.2  Angular Momentum of the Conical Pendulum .............. 237
   6.3  Central Force Motion and the Law of Equal Areas ....... 240
6.4  Capture Cross Section of a Planet ..................... 241
   6.5  Torque on a Sliding Block ............................. 244
   6.6  Torque on the Conical Pendulum ........................ 245
   6.7  Torque due to Gravity ................................. 247
   6.8  Moments of Inertia of Some Simple Objects ............. 250
   6.9  The Parallel Axis Theorem ............................. 252
   6.10 Atwood's Machine with a Massive Pulley ................ 254
   6.11 Grandfather's Clock ................................... 256
   6.12 Kater's Pendulum ...................................... 258
   6.13 The Doorstep .......................................... 259
   6.14 Angular Momentum of a Rolling Wheel ................... 262
   6.15 Disk on Ice ........................................... 264
   6.16 Drum Rolling down a Plane ............................. 265
   6.17 Drum Rolling down a Plane: Energy Method .............. 268
   6.18 The Falling Stick ..................................... 269

7  RIGID BODY L MOTION AND THE CONSERVATION OF ANGULAR
   MOMENTUM
   EXAMPLES, CHAPTER 7
   7.1  Rotations through Finite Angles ....................... 289
   7.2  Rotation in the xy Plane .............................. 291
   7.3  Vector Nature of Angular Velocity ..................... 291
   7.4  Angular Momentum of a Rotating Skew Rod ............... 292
   7.5  Torque on the Rotating Skew Rod ....................... 293
   7.6  Torque on the Rotating Skew Rod (Geometric Method) .... 294
   7.7  Gyroscope Precession .................................. 298
   7.8  Why a Gyroscope Precesses ............................. 299
   7.9  Precession of the Equinoxes ........................... 300
   7.10 The Gyrocompass Effect ................................ 301
   7.11 Gyrocompass Motion .................................... 302
   7.12 The Stability of Rotating Objects ..................... 304
   7.13 Rotating Dumbbell ..................................... 310
   7.14 The Tensor of Inertia for a Rotating Skew Rod ......... 312
   7.15 Why Flying Saucers Make Better Spacecraft than Do
        Flying Cigars ......................................... 314
   7.16 Stability of Rotational Motion ........................ 322
   7.17 The Rotating Rod ...................................... 323
   7.18 Euler's Equations and Torque-free Precession .......... 324

8  NONINERTIAL SYSTEMS AND FICTITIOUS FORCES
   EXAMPLES, CHAPTER 8
   8.1  The Apparent Force of Gravity ......................... 346
   8.2  Cylinder on an Accelerating Plank ..................... 347
   8.3  Pendulum in an Accelerating Car ....................... 347
   8.4  The Driving Force of the Tides ........................ 350
   8.5  Equilibrium Height of the Tide ........................ 352
   8.6  Surface of a Rotating Liquid .......................... 362
   8.7  The Coriolis Force .................................... 363
   8.8  Deflection of a Falling Mass .......................... 364
   8.9  Motion on the Rotating Earth .......................... 366
   8.10 Weather Systems ....................................... 366
   8.11 The Foucault Pendulum ................................. 369

9  CENTRAL FORCE MOTION
   EXAMPLES, CHAPTER 9
   9.1  Noninteracting Particles .............................. 384
   9.2  The Capture of Comets ................................. 387
   9.3  Perturbed Circular Orbit .............................. 388
   9.4  Hyperbolic Orbits ..................................... 393
   9.5  Satellite Orbit ....................................... 396
   9.6  Satellite Maneuver .................................... 398
   9.7  The Law of Periods .................................... 403

10 THE HARMONIC OSCILLATOR EXAMPLES, CHAPTER 10
   10.1 Initial Conditions and the Frictionless Harmonic
        Oscillator ............................................ 411
   10.2 The Q of Two Simple Oscillators ....................... 419
   10.3 Graphical Analysis of a Damped Oscillator ............. 420
   10.4 Forced Harmonic Oscillator Demonstration .............. 424
   10.5 Vibration Eliminator .................................. 428

11 THE SPECIAL THEORY OF RELATIVITY
   EXAMPLES, CHAPTER 11
   11.1 The Galilean Transformations .......................... 453
   11.2 A Light Pulse as Described by the Galilean
        Transformations ....................................... 455

12 RELATIVISTIC KINEMATICS
   EXAMPLES, CHAPTER 12
   12.1 Simultaneity .......................................... 463
   12.2 An Application of the Lorentz Transformations ......... 464
   12.3 The Order of Events: Timelike and Spacelike
        Intervals ............................................. 465
   12.4 The Orientation of a Moving Rod ....................... 467
   12.5 Time Dilation and Meson Decay ......................... 468
   12.6 The Role of Time Dilation in an Atomic Clock .......... 470
   12.7 The Speed of Light in a Moving Medium ................. 474
   12.8 Doppler Navigation .................................... 479

13 RELATIVISTIC MOMENTUM AND ENERGY
   EXAMPLES, CHAPTER 13
   13.1 Velocity Dependence of the Electron's Mass ............ 492
   13.2 Relativistic Energy and Momentum in an Inelastic
        Collision ............................................. 496
   13.3 The Equivalence of Mass and Energy .................... 498
   13.4 The Photoelectric Effect .............................. 502
   13.5 Radiation Pressure of Light ........................... 502
   13.6 The Compton Effect .................................... 503
   13.7 Pair Production ....................................... 505
   13.8 The Photon Picture of the Doppler Effect .............. 507
   13.9 The Rest Mass of the Photon ........................... 510
   13.10 Light from a Pulsar .................................. 510

14 FOUR-VECTORS AND RELATIVISTIC INVARIANCE
   EXAMPLES, CHAPTER 14
   14.1 Transformation Properties of the Vector Product ....... 518
   14.2 A Non-vector .......................................... 519
   14.3 Time Dilation ......................................... 524
   14.4 Construction of a Four-vector: The Four-velocity ...... 525
   14.5 The Relativistic Addition of Velocities ............... 526
   14.6 The Doppler Effect, Once More ......................... 530
   14.7 Relativistic Center of Mass Systems ................... 531
   14.8 Pair Production in Electron-electron Collisions ....... 533

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